Among 2.34, 2.43, 2.344 and 2.4, the greatest number is

1. 2.34

2. 2.43

3. 2.344

4. 2.4

Converting the given decimals into like decimals (3 decimal places):

2.340, 2.430, 2.344, 2.400

Clearly, 2.430 is the greatest. So, the greatest number is 2.43.

Hence, option 2 is the correct option.